Defining a family of functors
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Date:   (:) 
From:  Jacques Carette <carette@m...> 
Subject:  Re: [Camllist] Defining a family of functors 
Without the projections, you can do it via a higherorder Functor which does a fold, ie lifting to the Functor level what one usually does to get an nary product out of a binary product. With the projections, as this involves namegeneration, I don't see how to do it without using camlp4. Even my favourite sledgehammer, metocaml, can't help here. Jacques Michaël Grünewald wrote: > I am facing a situation that could be solved by ``defining a family of > functors'', I describe the problem and would be very glad to get your > views about it. > > To illustrate the situation, I will suppose A1, ..., An are modules > implementing the same signature S, let's say S contains the usual > opertations on groups (mathematical groups, you can replace this by > vector spaces, or whatever). It is easy to write a Product2 functor > > Product2: A1:S > A2:S > S2 > > producing an implementation for the direct product (with signature S) > of the groups A1 and A2, plus injections j1 : A1.t > S2.t and j2: > A2.t > S2.t and corresponding projections (the type t denotes the > module thingie, as usual). This extension of S is here written S2. > > My problem is ``how do I remove the 2'' ? Would it be possible to > define a functor scheme [:)] > > Productn: A1:S > .. > An:S > Sn > > able to instantiate concrete functors for any value of n ? > > It is possible to generate automatically appropriate code for small > values of n, but I am looking for a better approach. It is simple to > get close of the solution in the object paradigm, since I can simply > put objects in an array and iterate over this array (IIRC this is the > aggregate design pattern), but I do not see an easy way to define > injections and projections.